Sorry for the unhelpful subject line, but anything else that I tried was just

too long or too vague.

I have linked to Henri Cohen's paper which, among other things, shows how to

compute certain sums over primes:

http://www.math.u-bordeaux.fr/~cohen/hardylw.dvi
It turns out that the sum over all primes x < p of log(x)/x diverges to log(p)

+ k, a constant, which I've computed to 4-digit accuracy (I believe) as

-1.332 by the rather brute force-ish method of computing the sum over all

primes up to a billion.

Cohen's technique can evaluate sums of similar forms, but I can't tell if it

works for this particular one. I have reason to believe so, because in page 5

it reads: `By taking derivatives or limits, in an analogous manner we easily

compute:' and the first example is the sum over all primes of log(p)/p^2. It

turns out that the derivative of log(p)/p is log(p)/p^2 + 1. However, Cohen's

comment about derivatives is completely over my head, but I sense there's a

connection.

So, can anyone help out to derive a fast formula for the sum of log(x)/x over

primes using Cohen's technique? (or any other technique, for that matter)

Décio

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